# Circulation of a stream function

1. Sep 14, 2010

### marklar13

1. The problem statement, all variables and given/known data
The stream function of a 2D incompressible flow is given by:

$$\Psi$$=($$\Gamma$$/2pi)*ln(r)

Show that the circulation about a closed path about the origin is $$\Gamma$$ and is independent of r.

2. Relevant equations

$$\Gamma$$=-$$\oint$$V dot ds

3. The attempt at a solution

So far I know that the radial velocity component Ur=(1/r)*d(Psi)/d(theta)=0 because Psi does not depend on theta.
This means that the angular velocity component is the only velocity component: Utheta=-d(Psi)/d(r)=-L/2pi(r)
After this point im not exactly sure what to do.

Last edited: Sep 14, 2010
2. Sep 14, 2010

### marklar13

Cant really understand the latex stuff... working on it